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01.12.2014

Cameron–Liebler line classes in \(PG(n,4)\)

verfasst von: Alexander L. Gavrilyuk, Ivan Yu. Mogilnykh

Erschienen in: Designs, Codes and Cryptography | Ausgabe 3/2014

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We derive a new existence condition for Cameron–Liebler line classes in \(PG(3,q)\). As an application, we obtain the characterization of Cameron–Liebler line classes in \(PG(n,4),\,n\ge 3\).

Vorheriger Artikel A construction for strength-3 covering arrays from linear feedback shift register sequences

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Bamberg J.: There is no Cameron–Liebler line class of \(PG(3,4)\) with parameter 6. http://symomega.wordpress.com/2012/04/01/there-is-no-cameron-liebler-line-class-of-pg34-with-parameter-6/. Acc- essed 6 June 2013.

Bamberg J., Penttila T.: Overgroups of cyclic Sylow subgroups of linear groups. Commun. Algebra 36, 2503–2543 (2008).

Brouwer A.E., Cohen A.M., Neumaier A.: Distance-Regular Graphs. Springer, Berlin (1989).

Bruen A.A., Drudge K.: The construction of Cameron–Liebler line classes in \(PG(3, q)\). Finite Fields Appl. 5, 35–45 (1999).

Cameron P.J., Liebler R.A.: Tactical decompositions and orbits of projective groups. Linear Algebra Appl. 46, 91–102 (1982).

De Beule J., Hallez A., Storme L.: A non-existence result on Cameron–Liebler line classes. J. Comb. Des. 16(4), 342–349 (2008).

Drudge K.: Extremal sets in projective and polar spaces. Ph.D. Thesis, University of Western Ontario (1998).

Drudge K.: On a conjecture of Cameron and Liebler. Eur. J. Comb. 20(4), 263–269 (1999).

Gavrilyuk A., Goryainov S.: On perfect 2-colorings of Johnson graphs \(J(v,3)\). J. Comb. Des. 21(6), 232–252 (2012).

10.

Govaerts P., Penttila T.: Cameron–Liebler line classes in \(PG(3,4)\). Bull. Belg. Math. Soc. 12, 793–804 (2005).

11.

Govaerts P., Storme L.: On Cameron–Liebler line classes. Adv. Geom. 4, 279–286 (2004).

12.

Martin W.J.: Completely regular designs. J. Comb. Des. 6(4), 261–273 (1998).

13.

Metsch K.: The non-existence of Cameron–Liebler line classes with parameter \(2<x \le q\). Bull. Lond. Math. Soc. 42, 991–996 (2010).

14.

Penttila T.: Cameron–Liebler line classes in \(PG(3, q)\). Geom Dedicata 37, 245–252 (1991).

15.

Rodgers M.: Cameron–Liebler line classes. Des. Codes Cryptogr. 68, 33–37 (2011). doi:10.1007/s10623-011-9581-2.

16.

Sachkov V.N., Tarakanov V.E.: Combinatorics of nonnegative matrices. AMS, Providence (2002).

17.

Vanhove F.: Incidence geometry from an algebraic graph theory point of view. Ph.D. Thesis, University of Ghent (2011).

Titel: Cameron–Liebler line classes in
verfasst von: Alexander L. Gavrilyuk
Ivan Yu. Mogilnykh
Publikationsdatum: 01.12.2014
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 3/2014
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-013-9838-z

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Cameron–Liebler line classes in \(PG(n,4)\)

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